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Full text of "Mathematical And Physical Papers - Iii"

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SECTION II. Bands formed by a plane mirror, and viewed directly by the eye.
8. In the case of a plane mirror p = oo ; and if & be the retardation of the stream scattered at emergence relatively to the stream scattered at entrance, R will be obtained by adding together the second members of equations (5) and (11). Hence we have
It is to be remembered that in this formula a, b, c denote the co-ordinates of the luminous point; x, y those of any point in the dimmed surface ; a, b'y c' those of any point M of space towards which the eye is directed, and for distinct vision of which it is adapted; and that the formula is only approximate, the approximation depending both upon the smallness of the obliquity, and upon the smallness of the thickness t of the glass in comparison with the distances of the luminous point and the point M from the mirror.
As regards the illumination at a given point M} we arc evidently concerned with so much only of the dimmed surface us lies within a cone having M for vertex and the pupil of the eye for base ; and the bands will be seen distinctly if R do not alter by more than a small fraction of A, when xt y alter from one point to another of the portion of the dimmed surface which lies within this cone. Now we have seen already that the bands are in all cases seen distinctly in the neighbourhood of the image when the image itself is seen distinctly, so that when the image is real the bands may even be thrown on a screen, in which case a comparatively large portion of the dimmed surface is concerned in their formation. We may conclude that in the present case the bands will be seen with sufficient distinctness throughout, provided the image of the luminous point be seen distinctly.
9. In considering the distinctness or indistinctness of the bands, we are concerned with the finite size of the pupil of the eye; but in investigating only their form and magnitude we may